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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 427393, 12 pages
Application of Multistep Generalized Differential Transform Method for the Solutions of the Fractional-Order Chua's System
Department of Mathematics, Faculty of Science, The University of Jordan, Amman 1194, Jordan
Received 29 July 2012; Accepted 18 October 2012
Academic Editor: Mingshu Peng
Copyright © 2012 Asad Freihat and Shaher Momani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Sabatier, O. P. Agrawal, and J. A. Tenreiro Machado, Advances in Fractional Calculus; Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- C. Li and W. Deng, “Remarks on fractional derivatives,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 777–784, 2007.
- G. M. Zaslavsky, “Chaos, fractional kinetics, and anomalous transport,” Physics Reports, vol. 371, no. 6, pp. 461–580, 2002.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, Singapore, 2009.
- R. L. Bagley and P. J. Torvik, “A theoretical basis for the application of fractional calculus,” Journal of Rheology, vol. 27, pp. 201–210, 1983.
- R. L. Bagley and R. A. Calico, “Fractional order state equations for the control of viscoelastically damped structures,” Journal of Guidance, Control, and Dynamics, vol. 14, no. 2, pp. 304–311, 1991.
- E. J. S. Pires, J. A. T. Machado, and P. B. de Moura, “Fractional order dynamics in a GA planner,” Signal Processing, vol. 83, pp. 2377–2386, 2003.
- K. S. Hedrih and V. N. Stanojević, “A model of gear transmission: fractional order system dynamics,” Mathematical Problems in Engineering, vol. 2010, Article ID 972873, 2010.
- J. Cao, C. Ma, H. Xie, and Z. Jiang, “Nonlinear dynamics of duffing system with fractional order damping,” Journal of Computational and Nonlinear Dynamics, vol. 5, no. 4, pp. 041012–041018, 2010.
- C. Li and G. Chen, “Chaos and hyperchaos in the fractional-order Rössler equations,” Physica A, vol. 341, no. 1–4, pp. 55–61, 2004.
- K. Moaddy, S. Momani, and I. Hashim, “The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 1209–1216, 2011.
- A. G. Radwan, K. Moaddy, and S. Momani, “Stability and non-standard finite difference method of the generalized Chua's circuit,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 961–970, 2011.
- I. Petrás, “A note on the fractional-order Chua's system,” Chaos Solution & Fractals, vol. 38, pp. 140–147, 2008.
- T. T. Hartley, C. F. Lorenzo, and H. K. Qammer, “Chaos on a fractional Chua's system,” IEEE Transactions on Circuits and Systems, vol. 42, no. 8, pp. 485–490, 1995.
- Z. Odibat, S. Momani, and V. S. Erturk, “Generalized differential transform method: application to differential equations of fractional order,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 467–477, 2008.
- S. Momani and Z. Odibat, “A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor's formula,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 85–95, 2008.
- Z. Odibat and S. Momani, “A generalized differential transform method for linear partial differential equations of fractional order,” Applied Mathematics Letters, vol. 21, no. 2, pp. 194–199, 2008.
- V. S. Erturk, S. Momani, and Z. Odibat, “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1642–1654, 2008.
- Z. M. Odibat, C. Bertelle, M. A. Aziz-Alaoui, and G. H. E. Duchamp, “A multi-step differential transform method and application to non-chaotic or chaotic systems,” Computers & Mathematics with Applications, vol. 59, no. 4, pp. 1462–1472, 2010.
- V. S. Ertürk, Z. M. Odibat, and S. Momani, “An approximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of T-cells,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 996–1002, 2011.
- V. Erturk, G. Zaman, and S. Momani, “A numericanalytic method for approximating a giving up smoking model containing fractional derivatives,” Computers & Mathematics With Applications, vol. 64, no. 10, pp. 3065–3074, 2012.